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<p>We present a formulation of the three- and four-point amplitudes on the Coulomb branch of <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 4 SYM as integrals over the symplectic Grassmannian. We demonstrate that their kinematic spaces are equivalent to symplectic Grassmannians SpGr(<i>n</i>, 2<i>n</i>). For the three-point case, we express the amplitude as an integral over the symplectic Grassmannian in a specific little group frame. In the four-point case, we show that the integral yields the amplitude up to a known kinematic factor. Building on the four-dimensional analysis, we also express the six-dimensional <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = (1, 1) SYM amplitude in terms of four-dimensional variables in a form that makes its symplectic Grassmannian structure manifest.</p>

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Symplectic Grassmannian description of the Coulomb branch three and four point amplitudes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月10日

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  • Veronica Calvo Cortes,
  • Yassine El Maazouz,
  • Subramanya Hegde,
  • Amit Suthar

摘要

We present a formulation of the three- and four-point amplitudes on the Coulomb branch of N \( \mathcal{N} \) = 4 SYM as integrals over the symplectic Grassmannian. We demonstrate that their kinematic spaces are equivalent to symplectic Grassmannians SpGr(n, 2n). For the three-point case, we express the amplitude as an integral over the symplectic Grassmannian in a specific little group frame. In the four-point case, we show that the integral yields the amplitude up to a known kinematic factor. Building on the four-dimensional analysis, we also express the six-dimensional N \( \mathcal{N} \) = (1, 1) SYM amplitude in terms of four-dimensional variables in a form that makes its symplectic Grassmannian structure manifest.